
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
import statistics
import warnings
warnings.filterwarnings("ignore")


walmart = pd.read_csv("https://raw.githubusercontent.com/abinash25/Walmart_CaseStudy/refs/heads/main/Walmart_data.csv")
walmart


walmart.shape

(550068, 10)


walmart.dtypes

User_ID                        int64
Product_ID                    object
Gender                        object
Age                           object
Occupation                     int64
City_Category                 object
Stay_In_Current_City_Years    object
Marital_Status                 int64
Product_Category               int64
Purchase                       int64
dtype: object


walmart.nunique()

User_ID                        5891
Product_ID                     3631
Gender                            2
Age                               7
Occupation                       21
City_Category                     3
Stay_In_Current_City_Years        5
Marital_Status                    2
Product_Category                 20
Purchase                      18105
dtype: int64


walmart.isnull().sum()

User_ID                       0
Product_ID                    0
Gender                        0
Age                           0
Occupation                    0
City_Category                 0
Stay_In_Current_City_Years    0
Marital_Status                0
Product_Category              0
Purchase                      0
dtype: int64


walmart.duplicated().sum()

0


cat_col = ["User_ID", "Product_ID", "Gender", "Age", "City_Category", "Marital_Status"]

for i in cat_col:
    walmart[i] = walmart[i].astype("category")

walmart.dtypes

User_ID                       category
Product_ID                    category
Gender                        category
Age                           category
Occupation                       int64
City_Category                 category
Stay_In_Current_City_Years      object
Marital_Status                category
Product_Category                 int64
Purchase                         int64
dtype: object


walmart.describe().T


walmart.describe(include = ["object", "category"]).T


walmart.groupby(["Gender"])["User_ID"].nunique() / walmart["User_ID"].nunique() * 100

Gender
F    28.280428
M    71.719572
Name: User_ID, dtype: float64


walmart.groupby(["Gender"])["Purchase"].describe()


walmart.groupby(["Age"])["User_ID"].nunique() / walmart["User_ID"].nunique() * 100

Age
0-17      3.700560
18-25    18.146325
26-35    34.849771
36-45    19.809879
46-50     9.013750
51-55     8.164997
55+       6.314717
Name: User_ID, dtype: float64


walmart.groupby(["Age"])["Purchase"].describe()


walmart.groupby(["Stay_In_Current_City_Years"])["User_ID"].nunique()

Stay_In_Current_City_Years
0      772
1     2086
2     1145
3      979
4+     909
Name: User_ID, dtype: int64


walmart.groupby(["Marital_Status"])["User_ID"].nunique() / walmart["User_ID"].nunique() * 100

Marital_Status
0    58.003735
1    41.996265
Name: User_ID, dtype: float64


walmart.groupby(["City_Category"])["User_ID"].nunique()

City_Category
A    1045
B    1707
C    3139
Name: User_ID, dtype: int64


walmart.groupby(['City_Category'])['Purchase'].describe()


fig = plt.figure(figsize=(18,5))
sns.set_style("white")

plt.subplot(1, 2, 1)
sns.boxplot(data = walmart, x = "Purchase", orient = "h")

plt.title('Purchase Amount Analysis', fontsize = '14')


plt.subplot(1, 2, 2)
sns.distplot(a = walmart["Purchase"], color = 'gray')
plt.title("Distribution of Purchase Amount", fontsize = '14')
plt.axvline(walmart["Purchase"].mean(),color="g")
plt.axvline(walmart["Purchase"].median(),color="b")
plt.axvline(walmart["Purchase"].mode()[0],color="r")

plt.show()


print('Mean of Purchase Amount   = ', walmart["Purchase"].mean())
print('Median of Purchase Amount = ', walmart["Purchase"].median())

Mean of Purchase Amount   =  9263.968712959126
Median of Purchase Amount =  8047.0


q1 = walmart["Purchase"].quantile(0.25)
q3 = walmart["Purchase"].quantile(0.75)

IQR = q3 - q1
print("1. First Quartile (q1) = ", q1)
print("2. Third Quartile (q2) = ", q3)
print("3. IQR                 = ", IQR)

1. First Quartile (q1) =  5823.0
2. Third Quartile (q2) =  12054.0
3. IQR                 =  6231.0


walmart_new = walmart.copy()

# walmart_new = walmart_new.loc[(walmart_new["Purchase"] > q1 - 1.5*IQR) & (walmart_new["Purchase"] < q3 + 1.5*IQR)]
walmart_new["Purchase"] = np.clip(walmart_new["Purchase"], q1-1.5*IQR, q3 + 1.5*IQR)
walmart_new.shape

(550068, 10)


fig = plt.figure(figsize=(18,5))
sns.set_style("white")

plt.subplot(1, 2, 1)
sns.boxplot(data = walmart_new, x = "Purchase", orient = "h")

plt.title('Purchase Amount Analysis', fontsize = '14')


plt.subplot(1, 2, 2)
sns.distplot(a = walmart_new["Purchase"], color = 'gray')
plt.title("Distribution of Purchase Amount", fontsize = '14')
plt.axvline(walmart_new["Purchase"].mean(),color="g")
plt.axvline(walmart_new["Purchase"].median(),color="b")

plt.show()


fig = plt.figure(figsize=(18,10))
sns.set_style(style='white')
ax1 = plt.subplot2grid((2,2),(0,0))
sns.countplot(data=walmart_new, x="Gender", palette="crest")

#first row sec column
ax1 = plt.subplot2grid((2,2), (0, 1))
plt.pie(walmart_new["Gender"].value_counts(), 
        labels = walmart_new["Gender"].value_counts().index, 
        autopct = '%1.2f%%')
plt.suptitle('Distribution of Gender', fontsize = 20)

plt.show()


fig = plt.figure(figsize=(18,10))
sns.set_style(style='white')
ax1 = plt.subplot2grid((2,2),(0,0))
sns.countplot(data=walmart_new, x="Age", palette="crest")

#first row sec column
ax1 = plt.subplot2grid((2,2), (0, 1))
plt.pie(walmart_new["Age"].value_counts(), 
        labels = walmart_new["Age"].value_counts().index, 
        autopct = '%1.2f%%')
plt.suptitle('Distribution of Age', fontsize = 20)

plt.show()


fig = plt.figure(figsize=(18,10))
sns.set_style(style='white')
ax1 = plt.subplot2grid((2,2),(0,0))
sns.countplot(data=walmart, x="Marital_Status", palette="crest")

#first row sec column
ax1 = plt.subplot2grid((2,2), (0, 1))
plt.pie(walmart_new["Marital_Status"].value_counts(), 
        labels = walmart_new["Marital_Status"].value_counts().index, 
        autopct = '%1.2f%%')
plt.suptitle('Distribution of Marital_Status', fontsize = 20)

plt.show()


fig = plt.figure(figsize=(18,10))
sns.set_style(style='white')
ax1 = plt.subplot2grid((2,2),(0,0))
sns.countplot(data=walmart_new, x="City_Category", palette="crest")

#first row sec column
ax1 = plt.subplot2grid((2,2), (0, 1))
plt.pie(walmart_new["City_Category"].value_counts(), 
        labels = walmart_new["City_Category"].value_counts().index, 
        autopct = '%1.2f%%')
plt.suptitle('Distribution of City_Category', fontsize = 20)

plt.show()


fig = plt.figure(figsize=(18,10))
sns.set_style(style='white')
ax1 = plt.subplot2grid((2,2),(0,0))
sns.countplot(data=walmart_new, x="Stay_In_Current_City_Years", palette="crest")

#first row sec column
ax1 = plt.subplot2grid((2,2), (0, 1))
plt.pie(walmart_new["Stay_In_Current_City_Years"].value_counts(), 
        labels = walmart_new["Stay_In_Current_City_Years"].value_counts().index, 
        autopct = '%1.2f%%')
plt.suptitle('Distribution of Stay_In_Current_City_Years', fontsize = 20)
plt.show()


fig = plt.figure(figsize = (15,5))

sns.countplot(data = walmart_new, x = "Product_Category", palette="crest")
plt.xlabel("Product Category", fontsize = 15)
plt.title("Analysis of Product Category")
plt.show()


cat_col = ["Gender", "Marital_Status", "City_Category", "Age"]

fig, axs = plt.subplots(nrows=2, ncols = 2, figsize=(15,10))
k = 0
sns.set_style("dark")
for i in range(2):
    for j in range(2):
        sns.boxplot(data=walmart_new, x=cat_col[k], y="Purchase", palette='crest', ax=axs[i, j])
        axs[i, j].set_title("Purchase vs " + cat_col[k], pad = 10, fontsize = 14)
        k += 1
plt.show()


fig = plt.figure(figsize=(18, 15))

sns.set_style("white")

ax1 = plt.subplot2grid((2, 2), (0, 0))
sns.barplot(data=walmart_new, x = "Age", y = "Purchase", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Gender Analysis Purchase vs Age", pad = 10, fontsize = 14)

ax1 = plt.subplot2grid((2, 2), (0, 1))
sns.barplot(data=walmart_new, x = "Marital_Status", y = "Purchase", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Gender Analysis Purchase vs Marital Status", pad = 10, fontsize = 14)

ax1 = plt.subplot2grid((2, 2), (1, 0))
sns.barplot(data=walmart_new, x = "City_Category", y = "Purchase", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Gender Analysis Purchase vs City Category", pad = 10, fontsize = 14)

plt.show()


fig = plt.figure(figsize=(18, 15))

sns.set_style("white")

ax1 = plt.subplot2grid((2, 2), (0, 0))
sns.countplot(data=walmart_new, x = "Age", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Age Chrun Status", pad = 10, fontsize = 14)

ax1 = plt.subplot2grid((2, 2), (0, 1))
sns.countplot(data=walmart_new, x = "Marital_Status", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Marital Chrun Status", pad = 10, fontsize = 14)

ax1 = plt.subplot2grid((2, 2), (1, 0))
sns.countplot(data=walmart_new, x = "City_Category", ax=ax1, hue = "Gender", palette="crest")        
plt.title("City Category Churn Status", pad = 10, fontsize = 14)

ax1 = plt.subplot2grid((2, 2), (1, 1))
sns.countplot(data=walmart_new, x = "Stay_In_Current_City_Years", ax=ax1, hue = "Gender", palette="crest")        
plt.title("Stay_In_Current_City_Years Churn Status", pad = 10, fontsize = 14)

plt.show()


fig = plt.figure(figsize=(18, 5))

plt.title("Product Category analysis", fontsize = 15)
sns.countplot(data=walmart_new, x = "Product_Category", hue = "Gender", palette="crest")

plt.show()


fig = plt.figure(figsize=(18, 5))

plt.title("Box plot for city category for difference age brackets", fontsize = 15)
sns.boxplot(data=walmart_new, x = "Age", y = "Purchase", hue = "City_Category", palette="Set2")

plt.legend(loc = "upper right")
plt.show()


walmart_new.corr()


plt.figure(figsize = (15, 5))
sns.heatmap(data=walmart_new.corr(), annot=True, cmap="Blues", square=True)

sns.pairplot(walmart_new)
plt.show()


walmart_new.groupby(["Gender", "City_Category"])["User_ID"].count()

Gender  City_Category
F       A                 35704
        B                 57796
        C                 42309
M       A                112016
        B                173377
        C                128866
Name: User_ID, dtype: int64


plt.figure(figsize=(12, 7))

plt.title("Spending money per transction", fontsize = 15)
sns.histplot(data=walmart_new, x = "Purchase", bins=20, hue = "Gender", element="poly")

plt.show()


walmart_new.sample(5000, replace=True).groupby(["Gender"])["Purchase"].describe()


walmart_new.groupby(["Gender"])["Purchase"].describe()


walmart_new.shape

(550068, 10)


walmart_new_smp_male = walmart_new.loc[walmart["Gender"] == "M"]["Purchase"]
walmart_new_smp_female = walmart_new.loc[walmart["Gender"] == "F"]["Purchase"]


print("Male customers are: ", walmart_new_smp_male.shape[0])
print("Female customers are: ", walmart_new_smp_female.shape[0])

Male customers are:  414259
Female customers are:  135809


def bootstrapping_gender_purchase(sample1,sample2,smp_siz=500,itr_size=5000,confidence_level=0.95,no_of_tails=2):
    smp1_means_m = np.empty(itr_size)
    smp2_means_m = np.empty(itr_size)
    for i in range(itr_size):
        smp1_n = np.empty(smp_siz)
        smp2_n = np.empty(smp_siz)
        smp1_n = np.random.choice(sample1, size = smp_siz,replace=True)
        smp2_n = np.random.choice(sample2, size = smp_siz,replace=True)
        smp1_means_m[i] = np.mean(smp1_n)
        smp2_means_m[i] = np.mean(smp2_n)
        
    #Calcualte the Z-Critical value
    alpha = (1 - confidence_level)/no_of_tails
    z_critical = stats.norm.ppf(1 - alpha)
        
    # Calculate the mean, standard deviation & standard Error of sampling distribution of a sample mean
    mean1  = np.mean(smp1_means_m)
    sigma1 = np.std(smp1_means_m)
    sem1   = stats.sem(smp1_means_m)
    
    lower_limit1 = mean1 - (z_critical * sigma1)
    upper_limit1 = mean1 + (z_critical * sigma1)
    
    # Calculate the mean, standard deviation & standard Error of sampling distribution of a sample mean
    mean2  = np.mean(smp2_means_m)
    sigma2 = np.std(smp2_means_m)
    sem2   = stats.sem(smp2_means_m)
    
    lower_limit2 = mean2 - (z_critical * sigma2)
    upper_limit2 = mean2 + (z_critical * sigma2)
        
    fig, ax = plt.subplots(figsize=(14,6))
    sns.set_style("white")
    
    sns.kdeplot(data=smp1_means_m,fill=True,linewidth=2)
    sns.kdeplot(data=smp2_means_m,fill=True,linewidth=2)
    
    label_mean1=("μ (Males) :  {:.2f}".format(mean1))
    label_ult1=("Lower Limit(M):  {:.2f}\nUpper Limit(M):   {:.2f}".format(lower_limit1,upper_limit1))
    label_mean2=("μ (Females):  {:.2f}".format(mean2))
    label_ult2=("Lower Limit(F):  {:.2f}\nUpper Limit(F):   {:.2f}".format(lower_limit2,upper_limit2))
    
    plt.title(f"{confidence_level * 100}% CI on sample size = {smp_siz}")
    plt.xlabel('Purchase')
    plt.axvline(mean1, color = 'y', linestyle = 'solid', linewidth = 2,label=label_mean1)
    plt.axvline(upper_limit1, color = 'r', linestyle = 'solid', linewidth = 2,label=label_ult1)
    plt.axvline(lower_limit1, color = 'r', linestyle = 'solid', linewidth = 2)
    plt.axvline(mean2, color = 'b', linestyle = 'dashdot', linewidth = 2,label=label_mean2)
    plt.axvline(upper_limit2, color = '#56B4E9', linestyle = 'dashdot', linewidth = 2,label=label_ult2)
    plt.axvline(lower_limit2, color = '#56B4E9', linestyle = 'dashdot', linewidth = 2)
    plt.legend(loc='best')
    
    plt.show()
    
    return smp1_means_m,smp2_means_m ,np.round(lower_limit1,2),np.round(upper_limit1,2),np.round(lower_limit2,2),np.round(upper_limit2,2)


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 5000, 100000]
ci = 0.90

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_f, ul_f = bootstrapping_gender_purchase(walmart_new_smp_male,walmart_new_smp_female,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['M', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),90]]), axis=0)
    array = np.append(array, np.array([['F', ll_f, ul_f, smp_siz, ([ll_f,ul_f]) ,(ul_f-ll_f),90]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Gender','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Gender"] == "M") & (overlap["Sample_Size"] > 300)]


overlap.loc[(overlap["Gender"] == "F") & (overlap["Sample_Size"] > 300)]


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 5000, 100000]
ci = 0.95

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_f, ul_f = bootstrapping_gender_purchase(walmart_new_smp_male,walmart_new_smp_female,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['M', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),95]]), axis=0)
    array = np.append(array, np.array([['F', ll_f, ul_f, smp_siz, ([ll_f,ul_f]) ,(ul_f-ll_f),95]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Gender','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Gender"] == "M") & (overlap["Sample_Size"] > 300)]


overlap.loc[(overlap["Gender"] == "F") & (overlap["Sample_Size"] > 300)]


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 5000, 100000]
ci = 0.99

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_f, ul_f = bootstrapping_gender_purchase(walmart_new_smp_male,walmart_new_smp_female,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['M', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),99]]), axis=0)
    array = np.append(array, np.array([['F', ll_f, ul_f, smp_siz, ([ll_f,ul_f]) ,(ul_f-ll_f),99]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Gender','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Gender"] == "M") & (overlap["Sample_Size"] > 300)]


overlap.loc[(overlap["Gender"] == "F") & (overlap["Sample_Size"] > 300)]


walmart_new.groupby(["Marital_Status"])["Purchase"].describe()


plt.figure(figsize = (12, 5))

sns.histplot(data = walmart, x = "Purchase", hue = "Marital_Status", element="poly", bins = 20)

plt.show()


def bootstrapping_marital_status(sample1,sample2,smp_siz=500,itr_size=5000,confidence_level=0.95,no_of_tails=2):
    
    smp1_means_m = np.empty(itr_size)
    smp2_means_m = np.empty(itr_size)
    for i in range(itr_size):
        smp1_n = np.empty(smp_siz)
        smp2_n = np.empty(smp_siz)
        smp1_n = np.random.choice(sample1, size = smp_siz,replace=True)
        smp2_n = np.random.choice(sample2, size = smp_siz,replace=True)
        smp1_means_m[i] = np.mean(smp1_n)
        smp2_means_m[i] = np.mean(smp2_n)

#     std_dev1 = np.std(sample1)
#     std_err1 = np.std(sample1,ddof=1)/np.sqrt(smp_siz)
#     std_dev2 = np.std(sample2)
#     std_err2 = np.std(sample2,ddof=1)/np.sqrt(smp_siz)
        
    #Calcualte the Z-Critical value
    alpha = (1 - confidence_level)/no_of_tails
    z_critical = stats.norm.ppf(1 - alpha)
        
    # Calculate the mean, standard deviation & standard Error of sampling distribution of a sample mean
    mean1  = np.mean(smp1_means_m)
    sigma1 = statistics.stdev(smp1_means_m)
    sem1   = stats.sem(smp1_means_m)
    
    lower_limit1 = mean1 - (z_critical * sigma1)
    upper_limit1 = mean1 + (z_critical * sigma1)
    
    # Calculate the mean, standard deviation & standard Error of sampling distribution of a sample mean
    mean2  = np.mean(smp2_means_m)
    sigma2 = statistics.stdev(smp2_means_m)
    sem2   = stats.sem(smp2_means_m)

#     print(smp_siz,std_dev1,std_err1,sem1)
#     print(smp_siz,std_dev2,std_err2,sem2)
    
    lower_limit2 = mean2 - (z_critical * sigma2)
    upper_limit2 = mean2 + (z_critical * sigma2)
        
    fig, ax = plt.subplots(figsize=(14,6))
    sns.set_style("white")
    
    sns.kdeplot(data=smp1_means_m,color="#467821",fill=True,linewidth=2)
    sns.kdeplot(data=smp2_means_m,color='#e5ae38',fill=True,linewidth=2)
    
    label_mean1=("μ (Married) :  {:.2f}".format(mean1))
    label_ult1=("Lower Limit(M):  {:.2f}\nUpper Limit(M):   {:.2f}".format(lower_limit1,upper_limit1))
    label_mean2=("μ (Unmarried):  {:.2f}".format(mean2))
    label_ult2=("Lower Limit(F):  {:.2f}\nUpper Limit(F):   {:.2f}".format(lower_limit2,upper_limit2))
    
    plt.title(f"{confidence_level*100}% CI on Sample Size = {smp_siz}")
    plt.xlabel('Purchase')
    plt.axvline(mean1, color = 'y', linestyle = 'solid', linewidth = 2,label=label_mean1)
    plt.axvline(upper_limit1, color = 'r', linestyle = 'solid', linewidth = 2,label=label_ult1)
    plt.axvline(lower_limit1, color = 'r', linestyle = 'solid', linewidth = 2)
    plt.axvline(mean2, color = 'b', linestyle = 'dashdot', linewidth = 2,label=label_mean2)
    plt.axvline(upper_limit2, color = '#56B4E9', linestyle = 'dashdot', linewidth = 2,label=label_ult2)
    plt.axvline(lower_limit2, color = '#56B4E9', linestyle = 'dashdot', linewidth = 2)
    plt.legend(loc='upper right')

    plt.show()
    
    return smp1_means_m,smp2_means_m ,np.round(lower_limit1,2),np.round(upper_limit1,2),np.round(lower_limit2,2),np.round(upper_limit2,2)


walmart_new_smp_married = walmart.loc[walmart_new["Marital_Status"] == 1]["Purchase"]
walmart_new_smp_unmarried = walmart.loc[walmart_new["Marital_Status"] == 0]["Purchase"]

print(f"Married Customers: {walmart_new_smp_married.shape[0]}\nUnmarried Customers: {walmart_new_smp_unmarried[0]}")

Married Customers: 225337
Unmarried Customers: 8370


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 100000]
ci = 0.90

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_u, ul_u = bootstrapping_marital_status(walmart_new_smp_married,walmart_new_smp_unmarried,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['Married', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),90]]), axis=0)
    array = np.append(array, np.array([['Unmarried', ll_u, ul_u, smp_siz, ([ll_u,ul_u]) ,(ul_u-ll_u),90]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Marital_Status','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Marital_Status"] == "Married") & (overlap["Sample_Size"] >= 300)]


overlap.loc[(overlap["Marital_Status"] == "Unmarried") & (overlap["Sample_Size"] >= 300)]


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 100000]
ci = 0.95

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_u, ul_u = bootstrapping_marital_status(walmart_new_smp_married,walmart_new_smp_unmarried,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['Married', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),95]]), axis=0)
    array = np.append(array, np.array([['Unmarried', ll_u, ul_u, smp_siz, ([ll_u,ul_u]) ,(ul_u-ll_u),95]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Marital_Status','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Marital_Status"] == "Married") & (overlap["Sample_Size"] >= 300)]


overlap.loc[(overlap["Marital_Status"] == "Unmarried") & (overlap["Sample_Size"] >= 300)]


itr_size = 1000
size_list = [1, 10, 30, 300, 1000, 100000]
ci = 0.99

array = np.empty((0,7))

for smp_siz in size_list:
    m_avg, f_avg, ll_m, ul_m, ll_u, ul_u = bootstrapping_marital_status(walmart_new_smp_married,walmart_new_smp_unmarried,smp_siz,itr_size,ci)

    array = np.append(array, np.array([['Married', ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),99]]), axis=0)
    array = np.append(array, np.array([['Unmarried', ll_u, ul_u, smp_siz, ([ll_u,ul_u]) ,(ul_u-ll_u),99]]), axis=0)

overlap = pd.DataFrame(array, columns = ['Marital_Status','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


overlap.loc[(overlap["Marital_Status"] == "Married") & (overlap["Sample_Size"] >= 300)]


overlap.loc[(overlap["Marital_Status"] == "Unmarried") & (overlap["Sample_Size"] >= 300)]


age_data = walmart_new.groupby(["Age"])["Purchase"].describe()


age_dict = {}
age_list = ['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+']

# Print the columns of age_data for debugging
print("Columns in age_data:", age_data.columns)

# Check that age_data has enough rows
num_ages = min(len(age_list), age_data.shape[0])

for i in range(num_ages):
    # Debug: Print the row being accessed
    print(f"Accessing row {i}: {age_data.iloc[i]}")
    
    # Adjust the column name if necessary
    try:
        age_dict[age_list[i]] = age_data.iloc[i]["Mean"]  # Adjust if column name differs
    except KeyError as e:
        print(f"KeyError: {e}. Check if the column name is correct.")

Columns in age_data: Index(['count', 'mean', 'std', 'min', '25%', '50%', '75%', 'max'], dtype='object')
Accessing row 0: count    15102.000000
mean      8925.539597
std       5090.078414
min         12.000000
25%       5328.000000
50%       7986.000000
75%      11874.000000
max      21400.500000
Name: 0-17, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 1: count    99660.000000
mean      9164.189554
std       5019.866472
min         12.000000
25%       5415.000000
50%       8027.000000
75%      12028.000000
max      21400.500000
Name: 18-25, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 2: count    219587.000000
mean       9244.947060
std        4990.086124
min          12.000000
25%        5475.000000
50%        8030.000000
75%       12047.000000
max       21400.500000
Name: 26-35, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 3: count    110013.000000
mean       9320.888550
std        4995.487782
min          12.000000
25%        5876.000000
50%        8061.000000
75%       12107.000000
max       21400.500000
Name: 36-45, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 4: count    45701.000000
mean      9198.531093
std       4940.249496
min         12.000000
25%       5888.000000
50%       8036.000000
75%      11997.000000
max      21400.500000
Name: 46-50, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 5: count    38501.000000
mean      9519.560427
std       5048.447704
min         12.000000
25%       6017.000000
50%       8130.000000
75%      12462.000000
max      21400.500000
Name: 51-55, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.
Accessing row 6: count    21504.000000
mean      9319.768741
std       4968.014656
min         12.000000
25%       6018.000000
50%       8105.500000
75%      11932.000000
max      21400.500000
Name: 55+, dtype: float64
KeyError: 'Mean'. Check if the column name is correct.


plt.figure(figsize = (12, 5))

sns.histplot(data = walmart_new, x = "Purchase", bins = 20, hue = "Age", element="poly")
plt.show()


def bootstrapping_age(sample,smp_siz=500,itr_size=5000,confidence_level=0.95,age= "0-17", no_of_tails=2):
    
    smp_means_m = np.empty(itr_size)
    for i in range(itr_size):
        smp_n = np.empty(smp_siz)
        smp_n = np.random.choice(sample, size = smp_siz,replace=True)
        smp_means_m[i] = np.mean(smp_n)
        
    #Calcualte the Z-Critical value
    alpha = (1 - confidence_level)/no_of_tails
    z_critical = stats.norm.ppf(1 - alpha)
        
    # Calculate the mean, standard deviation & standard Error of sampling distribution of a sample mean
    mean  = np.mean(smp_means_m)
    sigma = statistics.stdev(smp_means_m)
    sem   = stats.sem(smp_means_m)
    
    lower_limit = mean - (z_critical * sigma)
    upper_limit = mean + (z_critical * sigma)
       
    fig, ax = plt.subplots(figsize=(14,6))
    sns.set_style("darkgrid")
    
    sns.kdeplot(data=smp_means_m,color="#7A68A6",fill=True,linewidth=2)
    
    label_mean=("μ :  {:.2f}".format(mean))
    label_ult=("Lower Limit:  {:.2f}\nUpper Limit:   {:.2f}".format(lower_limit,upper_limit))
    
    plt.title(f"{confidence_level * 100} CI on sample size {smp_siz} on age bracket {age}")
    plt.xlabel('Purchase')
    plt.axvline(mean, color = 'y', linestyle = 'solid', linewidth = 2,label=label_mean)
    plt.axvline(upper_limit, color = 'r', linestyle = 'solid', linewidth = 2,label=label_ult)
    plt.axvline(lower_limit, color = 'r', linestyle = 'solid', linewidth = 2)
    plt.legend(loc='upper right')

    plt.show()
    
    return smp_means_m ,np.round(lower_limit,2),np.round(upper_limit,2)


itr_size = 1000
smp_size = 10000
ci = 0.90
age_list =['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 

array = np.empty((0,8))

for age in age_list:
    mean, ll_m, ul_m = bootstrapping_age(walmart_new[walmart_new['Age'] == age]['Purchase'],smp_siz,itr_size,ci, age)

    array = np.append(array, np.array([[age,np.round(mean,2), ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),90]]), axis=0)

age_data = pd.DataFrame(array, columns = ['Age_Group','Mean','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


age_dict = {}
age_list = ['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 
for i in range(len(age_data)):
    age_dict[age_list[i]] = age_data.loc[i, "Mean"]
    
fig, ax = plt.subplots(figsize=(14,6))
sns.set_style("darkgrid")
for label_val in age_dict.keys():
    sns.kdeplot(age_dict[label_val], shade = True, label = label_val)

plt.title("Sampling distribution of a sample mean for each Age for 90% CI",fontsize=14)
plt.xlabel('Purchase')
plt.legend(loc='upper right')

plt.show()


age_data.head(10)


itr_size = 1000
smp_size = 10000
ci = 0.95
age_list =['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 

array = np.empty((0,8))

for age in age_list:
    mean, ll_m, ul_m = bootstrapping_age(walmart_new[walmart_new['Age'] == age]['Purchase'],smp_siz,itr_size,ci, age)

    array = np.append(array, np.array([[age,np.round(mean,2), ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),95]]), axis=0)

age_data = pd.DataFrame(array, columns = ['Age_Group','Mean','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


age_dict = {}
age_list = ['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 
for i in range(len(age_data)):
    age_dict[age_list[i]] = age_data.loc[i, "Mean"]
    
fig, ax = plt.subplots(figsize=(14,6))
sns.set_style("darkgrid")
for label_val in age_dict.keys():
    sns.kdeplot(age_dict[label_val], shade = True, label = label_val)

plt.title("Sampling distribution of a sample mean for each Age for 95% CI",fontsize=14)
plt.xlabel('Purchase')
plt.legend(loc='upper right')

plt.show()


age_data.head(7)


itr_size = 1000
smp_size = 10000
ci = 0.99
age_list =['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 

array = np.empty((0,8))

for age in age_list:
    mean, ll_m, ul_m = bootstrapping_age(walmart_new[walmart_new['Age'] == age]['Purchase'],smp_siz,itr_size,ci, age)

    array = np.append(array, np.array([[age,np.round(mean,2), ll_m, ul_m, smp_siz, ([ll_m,ul_m]) ,(ul_m-ll_m),99]]), axis=0)

age_data = pd.DataFrame(array, columns = ['Age_Group','Mean','Lower_limit','Upper_limit','Sample_Size','CI','Range','Confidence_pct'])


age_dict = {}
age_list = ['0-17', '18-25', '26-35', '36-45', '46-50', '51-55', '55+'] 
for i in range(len(age_data)):
    age_dict[age_list[i]] = age_data.loc[i, "Mean"]
    
fig, ax = plt.subplots(figsize=(14,6))
sns.set_style("darkgrid")
for label_val in age_dict.keys():
    sns.kdeplot(age_dict[label_val], shade = True, label = label_val)

plt.title("Sampling distribution of a sample mean for each Age for 95% CI",fontsize=14)
plt.xlabel('Purchase')
plt.legend(loc='upper right')

plt.show()


age_data.head(7)

	User_ID	Product_ID	Gender	Age	Occupation	City_Category	Stay_In_Current_City_Years	Marital_Status	Product_Category	Purchase
0	1000001	P00069042	F	0-17	10	A	2	0	3	8370
1	1000001	P00248942	F	0-17	10	A	2	0	1	15200
2	1000001	P00087842	F	0-17	10	A	2	0	12	1422
3	1000001	P00085442	F	0-17	10	A	2	0	12	1057
4	1000002	P00285442	M	55+	16	C	4+	0	8	7969
...	...	...	...	...	...	...	...	...	...	...
550063	1006033	P00372445	M	51-55	13	B	1	1	20	368
550064	1006035	P00375436	F	26-35	1	C	3	0	20	371
550065	1006036	P00375436	F	26-35	15	B	4+	1	20	137
550066	1006038	P00375436	F	55+	1	C	2	0	20	365
550067	1006039	P00371644	F	46-50	0	B	4+	1	20	490

	count	mean	std	min	25%	50%	75%	max
Gender
F	135809.0	8734.565765	4767.233289	12.0	5433.0	7914.0	11400.0	23959.0
M	414259.0	9437.526040	5092.186210	12.0	5863.0	8098.0	12454.0	23961.0

	count	mean	std	min	25%	50%	75%	max
City_Category
A	147720.0	8911.939216	4892.115238	12.0	5403.0	7931.0	11786.0	23961.0
B	231173.0	9151.300563	4955.496566	12.0	5460.0	8005.0	11986.0	23960.0
C	171175.0	9719.920993	5189.465121	12.0	6031.5	8585.0	13197.0	23961.0

	count	mean	std	min	25%	50%	75%	max
Gender
F	1276.0	8686.983542	4857.656372	37.0	5386.50	7870.0	11053.0	21400.5
M	3724.0	9452.649570	5100.822250	13.0	5480.75	8099.0	12632.5	21400.5

	Age_Group	Mean	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
0	0-17	[8941.35, 8944.93, 8924.8, 8940.68, 8926.98, 8...	8898.89	8952.47	100000	[8898.89, 8952.47]	53.58	90
1	18-25	[9158.29, 9163.78, 9148.03, 9145.51, 9187.84, ...	9139.09	9190.64	100000	[9139.09, 9190.64]	51.55	90
2	26-35	[9217.29, 9246.88, 9234.6, 9237.24, 9257.65, 9...	9219.24	9270.79	100000	[9219.24, 9270.79]	51.55	90
3	36-45	[9311.72, 9277.78, 9313.8, 9321.94, 9300.1, 93...	9295.38	9346.93	100000	[9295.38, 9346.93]	51.55	90
4	46-50	[9178.59, 9211.77, 9165.91, 9178.5, 9206.45, 9...	9172.09	9225.16	100000	[9172.09, 9225.16]	53.07	90
5	51-55	[9509.98, 9510.0, 9506.27, 9518.82, 9513.11, 9...	9494.2	9544.36	100000	[9494.2, 9544.36]	50.16	90
6	55+	[9320.55, 9315.74, 9352.57, 9337.68, 9312.58, ...	9293.35	9344.12	100000	[9293.35, 9344.12]	50.77	90

	count	mean	std	min	25%	50%	75%	max
Occupation	550068.0	8.076707	6.522660	0.0	2.0	7.0	14.0	20.0
Product_Category	550068.0	5.404270	3.936211	1.0	1.0	5.0	8.0	20.0
Purchase	550068.0	9263.968713	5023.065394	12.0	5823.0	8047.0	12054.0	23961.0

	count	unique	top	freq
User_ID	550068	5891	1001680	1026
Product_ID	550068	3631	P00265242	1880
Gender	550068	2	M	414259
Age	550068	7	26-35	219587
City_Category	550068	3	B	231173
Stay_In_Current_City_Years	550068	5	1	193821
Marital_Status	550068	2	0	324731

	count	mean	std	min	25%	50%	75%	max
Age
0-17	15102.0	8933.464640	5111.114046	12.0	5328.0	7986.0	11874.0	23955.0
18-25	99660.0	9169.663606	5034.321997	12.0	5415.0	8027.0	12028.0	23958.0
26-35	219587.0	9252.690633	5010.527303	12.0	5475.0	8030.0	12047.0	23961.0
36-45	110013.0	9331.350695	5022.923879	12.0	5876.0	8061.0	12107.0	23960.0
46-50	45701.0	9208.625697	4967.216367	12.0	5888.0	8036.0	11997.0	23960.0
51-55	38501.0	9534.808031	5087.368080	12.0	6017.0	8130.0	12462.0	23960.0
55+	21504.0	9336.280459	5011.493996	12.0	6018.0	8105.5	11932.0	23960.0

	Occupation	Product_Category	Purchase
Occupation	1.000000	-0.007618	0.020853
Product_Category	-0.007618	1.000000	-0.347413
Purchase	0.020853	-0.347413	1.000000

	count	mean	std	min	25%	50%	75%	max
Gender
F	135809.0	8726.256327	4743.242716	12.0	5433.0	7914.0	11400.0	21400.5
M	414259.0	9428.373455	5068.732811	12.0	5863.0	8098.0	12454.0	21400.5

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
8	M	9155.11	9698.62	1000	[9155.11, 9698.62]	543.51	90
10	M	9313.01	9548.53	5000	[9313.01, 9548.53]	235.52	90
12	M	9401.74	9453.95	100000	[9401.74, 9453.95]	52.21	90

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
9	F	8485.28	8975.63	1000	[8485.28, 8975.63]	490.35	90
11	F	8611.72	8839.65	5000	[8611.72, 8839.65]	227.93	90
13	F	8701.73	8751.81	100000	[8701.73, 8751.81]	50.08	90

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
8	M	9106.81	9746.32	1000	[9106.81, 9746.32]	639.51	95
10	M	9284.33	9564.21	5000	[9284.33, 9564.21]	279.88	95
12	M	9396.45	9461.03	100000	[9396.45, 9461.03]	64.58	95

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
9	F	8433.19	9013.3	1000	[8433.19, 9013.3]	580.11	95
11	F	8591.57	8860.48	5000	[8591.57, 8860.48]	268.91	95
13	F	8696.34	8755.65	100000	[8696.34, 8755.65]	59.31	95

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
8	M	9000.78	9848.31	1000	[9000.78, 9848.31]	847.53	99
10	M	9246.06	9605.58	5000	[9246.06, 9605.58]	359.52	99
12	M	9386.64	9469.1	100000	[9386.64, 9469.1]	82.46	99

	Gender	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
9	F	8357.14	9098.16	1000	[8357.14, 9098.16]	741.02	99
11	F	8565.21	8893.56	5000	[8565.21, 8893.56]	328.35	99
13	F	8687.86	8764.53	100000	[8687.86, 8764.53]	76.67	99

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
6	Married	8778.3	9728.0	300	[8778.3, 9728.0]	949.7	90
8	Married	8993.18	9527.68	1000	[8993.18, 9527.68]	534.5	90
10	Married	9235.24	9286.38	100000	[9235.24, 9286.38]	51.14	90

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
7	Unmarried	8788.42	9739.38	300	[8788.42, 9739.38]	950.96	90
9	Unmarried	9008.2	9532.84	1000	[9008.2, 9532.84]	524.64	90
11	Unmarried	9239.92	9292.87	100000	[9239.92, 9292.87]	52.95	90

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
6	Married	8675.75	9839.68	300	[8675.75, 9839.68]	1163.93	95
8	Married	8948.48	9567.36	1000	[8948.48, 9567.36]	618.88	95
10	Married	9230.44	9292.36	100000	[9230.44, 9292.36]	61.92	95

	count	mean	std	min	25%	50%	75%	max
Marital_Status
0	324731.0	9257.517959	5005.287278	12.0	5605.0	8044.0	12061.0	21400.5
1	225337.0	9251.430702	4991.196933	12.0	5843.0	8051.0	12042.0	21400.5

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
7	Unmarried	8706.42	9818.34	300	[8706.42, 9818.34]	1111.92	95
9	Unmarried	8941.04	9579.59	1000	[8941.04, 9579.59]	638.55	95
11	Unmarried	9233.8	9298.35	100000	[9233.8, 9298.35]	64.55	95

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
6	Married	8484.77	10013.31	300	[8484.77, 10013.31]	1528.54	99
8	Married	8844.05	9672.66	1000	[8844.05, 9672.66]	828.61	99
10	Married	9217.81	9301.8	100000	[9217.81, 9301.8]	83.99	99

	Marital_Status	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
7	Unmarried	8516.8	9997.26	300	[8516.8, 9997.26]	1480.46	99
9	Unmarried	8862.96	9671.87	1000	[8862.96, 9671.87]	808.91	99
11	Unmarried	9226.34	9306.08	100000	[9226.34, 9306.08]	79.74	99

	Age_Group	Mean	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
0	0-17	[8947.89, 8942.76, 8925.93, 8915.89, 8912.76, ...	8894.48	8957.47	100000	[8894.48, 8957.47]	62.99	95
1	18-25	[9183.68, 9189.49, 9155.77, 9186.09, 9179.09, ...	9132.79	9194.94	100000	[9132.79, 9194.94]	62.15	95
2	26-35	[9252.98, 9218.91, 9234.28, 9235.98, 9258.41, ...	9215.01	9275.27	100000	[9215.01, 9275.27]	60.26	95
3	36-45	[9323.51, 9311.93, 9322.01, 9325.35, 9303.73, ...	9290.15	9352.13	100000	[9290.15, 9352.13]	61.98	95
4	46-50	[9206.01, 9221.36, 9172.65, 9196.1, 9214.81, 9...	9168.04	9228.77	100000	[9168.04, 9228.77]	60.73	95
5	51-55	[9540.11, 9535.16, 9553.96, 9540.37, 9514.08, ...	9486.49	9552.72	100000	[9486.49, 9552.72]	66.23	95
6	55+	[9321.24, 9302.96, 9324.06, 9312.92, 9320.13, ...	9290.47	9350.39	100000	[9290.47, 9350.39]	59.92	95

	Age_Group	Mean	Lower_limit	Upper_limit	Sample_Size	CI	Range	Confidence_pct
0	0-17	[8928.29, 8922.77, 8916.81, 8906.55, 8919.38, ...	8884.34	8967.09	100000	[8884.34, 8967.09]	82.75	99
1	18-25	[9134.7, 9173.27, 9161.54, 9178.74, 9170.43, 9...	9123.61	9203.97	100000	[9123.61, 9203.97]	80.36	99
2	26-35	[9257.45, 9225.01, 9240.23, 9255.58, 9235.93, ...	9204.04	9285.27	100000	[9204.04, 9285.27]	81.23	99
3	36-45	[9313.53, 9328.46, 9300.9, 9342.83, 9318.04, 9...	9279.22	9362.72	100000	[9279.22, 9362.72]	83.5	99
4	46-50	[9197.02, 9189.32, 9221.9, 9179.71, 9175.52, 9...	9158.68	9239.15	100000	[9158.68, 9239.15]	80.47	99
5	51-55	[9542.91, 9534.92, 9537.76, 9531.29, 9510.16, ...	9478.42	9561.54	100000	[9478.42, 9561.54]	83.12	99
6	55+	[9318.33, 9309.57, 9332.09, 9334.56, 9325.97, ...	9279.41	9359.9	100000	[9279.41, 9359.9]	80.49	99

Problem Statement¶

Installing Dependencies¶

Loading Dataset¶

Shape of Data¶

Datatype of features¶

Unique Value (counts) for each features¶

Missing Values Detection¶

Validating duplicate values¶

Statistical Summary¶

Non-Graphical Analysis¶

Value counts and Unique Attributes¶

Graphical Analysis¶

Univariate Countinous Variable Analysis¶

Detecting Outliers¶

Handling Outliers¶

Univariate Categorical Variable Analysis¶

Bivariate Analysis¶

Lets draw analysis for Gender¶

Lets draw analysis for City Category Among Different Age Brackets¶

Correlation Analysis¶

4. Answering questions¶

4.1 Are women spending more money per transaction than men? Why or Why not?¶

Lets take sample of data to verify this fact¶

4.2 Confidence intervals and distribution of the mean of the expenses by female and male customers¶

Calculating CI (90%, 95%, 99%) using Bootstrapping for Puchases based on Gender using CLT¶

Calculation 90% CI¶

Calculate 95% CI¶

Calculate 99% CI¶

4.3 Are confidence intervals of average male and female spending overlapping? How can Walmart leverage this conclusion to make changes or improvements?¶

Answer¶

Conclusion to make changes and improvements¶

4.4 Results when the same activity is performed for Married vs Unmarried¶

Calculating CI (90%, 95%, 99%) using Bootstrapping for Puchases based on Marital_Status using CLT¶

Calculating 90% CI¶

Calculating 95% CI¶

Calculating 99% CI¶

Major Inferences¶

4.5 Results when the same activity is performed for Age¶

Calculate CI (90%, 95%, 99%) for purchase based on age using CLT¶

Calculating 90% CI¶

Checking the Sampling distribution of a sample mean for each Age Group for 90% CI¶

Calculating 95% CI¶

Checking the Sampling distribution of a sample mean for each Age Group for 95% CI¶

Calculating 99% CI¶

Checking the Sampling distribution of a sample mean for each Age Group for 99% CI¶

Major Inferences¶

5. Final Insights¶

Based on EDA¶

Based on CLT & CI¶

6. Recommendations¶